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In two dimensions I am under the impression that the ricci tensor or the scalar curvature equals the negative of the fundamental tensor and the sectional curvature (K).

I'd have written it out with the proper symbols but I am new to this forum and this isn't at least a complex question.

I know that the sectional curvature is directly proportional to the Riemannian Tensor, and since I am only talking about two dimensions, the only term that is independent and nonzero is R 1212. OK with the symmetries there are dependent terms that are the positive and negative of that but all of the multiplicities cancel out in the definition of K.

I was wondering if there where was anyone out there who can walk me or US through how this equation is true?

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# Ricci and K (curvature)

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